The Ivory Coast international had equalised with a fine, curling effort to cancel out Teemu Pukki's 39-second opener for the home side. But the game would finish 1-1 as Zaha wasted the chance to claim all three points, horribly scuffing a spot-kick just minutes after his individual strike.
"As I ran up I felt my left foot slip as I went to stand before shooting," he told Palace TV.
"As soon as I felt it go, I thought: 'This is definitely not going to go where I want it to'.
"You've just got to get over it. In football you haven't got time to cry about it. I was asked if I got another pen whether I would stand up and take it - 100 per cent. I've got the confidence to go up and take it, and I've just got to make sure I score next time."